(a) Consider the following.
Write the percent represented by the shaded portion of the grid.
%
Find that percent of the given number.
72,200
(b) Consider the following.
Write the percent represented by the shaded portion of the grid.
%

The factors of g are (x - 10) and (x + 2), which confirms that the zeros are 10 and -2.

The positive integers that can divide a number evenly are referred to as factors.  Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element.  There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.

The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (-1). The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.

The zeros are 10 and -2, because the factors of g are (x-10) and (x + 2).

To find the zeros, we can set g(x) equal to zero and solve for x:

x² - 8x - 20 = 0

Using the quadratic formula, we get:

x = [8 ± √(8² + 4(1)(20))] / 2

x = [8 ± √144] / 2

x = [8 ± 12] / 2

So, the zeros are:

x = 10 and x = -2

We can verify this by factoring g(x):

g(x) = x² - 8x - 20

g(x) = (x - 10)(x + 2)

So, the factors of g are (x - 10) and (x + 2), which confirms that the zeros are 10 and -2.

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Answer:

Sphere Volume = (4/3) * PI radius^3

Sphere Volume = (4/3) * 3 * 3 * 3 * PI =

4 * 3 * 3 * PI =

36 PI

Answer is d 36 PI cubic feet

Step-by-step explanation:

Answer:

1/4 −2+ −21/4 =1/2

(Decimal: 0.5)

Step-by-step explanation:

Answer:

\(A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}\)

Step-by-step explanation:

Given

Let the two triangles be A and B

Sides of A: 4, 6 and 8.5

Sides of B: 6, 9 and 12.5

Required

Which set of ratio determines the dilation

To determine the dilation of  a triangle over another;

We simply divide the side of a triangle by a similar side on the other triangle;

From the given parameters,

A ------------------B

4 is similar to 6

6 is similar to 9

8.5 is similar to 12.5

Ratio of dilation is as follows;

\(Dilation = \frac{4}{6}\)

\(Dilation = \frac{6}{9}\)

\(Dilation = \frac{8.5}{12.5}\)

Combining the above ratios;

\(Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}\)

From the list of given options, the correct option is A,

Answer:

a

Step-by-step explanation:

Thus, (-12, -29, 21) is a vector that is orthogonal to both (7,0,4) and (-7,3,1).

To find a vector that is orthogonal (or perpendicular) to the two given vectors, we can use the cross product of the two vectors. The cross product of two vectors, denoted by a × b, gives a vector that is orthogonal to both a and b.

So, let's take the two given vectors:

a = (7,0,4)
b = (-7,3,1)

To find a vector orthogonal to a and b, we can take their cross product:

a × b =
(0 * 1 - 4 * 3, 4 * (-7) - 7 * 1, 7 * 3 - 0 * (-7)) =
(-12, -29, 21)

Therefore, (-12, -29, 21) is a vector that is orthogonal to both (7,0,4) and (-7,3,1). Note that there are infinitely many vectors that are orthogonal to a given vector or a pair of vectors, since we can always add a scalar multiple of the given vector(s) to the orthogonal vector and still get a valid solution.

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The domain of the function C(m) = 0.05m + 20 is (0, ∞) and the range of the function C(m) = 0.05m + 20 is (20, ∞).

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. The total cost of Haley’s monthly cell phone bill can be expressed by the function

\(\rm C(m) = 0.05\ m + 20\)

The domain of the function is from zero to infinity because time can never be negative.

Then the range of the function will be

At m = 0, the value of C(m) will be

C(m) = 0.05(0) + 20

C(m) = 20

At m = ∞, the value of C(m) will be

C(m) = 0.05(∞) + 20

C(m) = ∞

Thus, the domain of the function is (0, ∞) and the range of the function is (20, ∞).

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Answer:

Evaluate ∫3x2sin(x3)cos(x3)dx

Step-by-step explanation:

hello        (a) using the substitution u=sin(x3)  because

du =3x²(cos x3)dx

you have   ∫3x2sin(x3)cos(x3)dx = ∫udu=u²/2 +c............continu

(a) Using a t-test approach and a 5% level of significance, the slope coefficient is significantly positive.

(b) (i) The coefficient of intercept is significantly different from zero at a 1% level of significance.

(ii) The slope coefficient is significantly different from one at a 5% level of significance.

(c) The p-value for the coefficient of intercept is less than 0.01, providing strong evidence against the null hypothesis.

(d) The p-value for the slope coefficient is less than 0.05, indicating a significant deviation from the value of one.

(a) To test if the slope coefficient can be positive, we can use a t-test approach with a 5% level of significance. The null and alternative hypotheses are as follows:

Null hypothesis (H0): The slope coefficient is zero (β1 = 0)

Alternative hypothesis (Ha): The slope coefficient is positive (β1 > 0)

We can use the t-statistic to test this hypothesis. The t-statistic is calculated by dividing the estimated coefficient by its standard error. In this case, the estimated coefficient for the slope is 0.73, and the standard error is 0.10 (based on the heteroskedasticity-robust standard error).

t-statistic = (0.73 - 0) / 0.10 = 7.3

Looking up the critical value in the t-table at a 5% level of significance for a two-tailed test (since we are testing for positive coefficient), we find that the critical value is approximately 1.660.

Since the calculated t-statistic (7.3) is greater than the critical value (1.660), we reject the null hypothesis. Therefore, there is sufficient evidence to suggest that the slope coefficient is positive.

(b) (i) To test if the coefficient of intercept is zero at a 1% level of significance, we can use a t-test. The null and alternative hypotheses are as follows:

Null hypothesis (H0): The coefficient of intercept is zero (β0 = 0)

Alternative hypothesis (Ha): The coefficient of intercept is not equal to zero (β0 ≠ 0)

Using the same t-test approach, we can calculate the t-statistic for the intercept coefficient. The estimated coefficient for the intercept is 19.6, and the standard error is 7.2.

t-statistic = (19.6 - 0) / 7.2 ≈ 2.722

Looking up the critical value in the t-table at a 1% level of significance for a two-tailed test, we find that the critical value is approximately 2.626.

Since the calculated t-statistic (2.722) is greater than the critical value (2.626), we reject the null hypothesis. Therefore, there is sufficient evidence to suggest that the coefficient of intercept is not equal to zero.

(ii) To test if the slope coefficient is 1 at a 5% level of significance, we can use a t-test. The null and alternative hypotheses are as follows:

Null hypothesis (H0): The slope coefficient is 1 (β1 = 1)

Alternative hypothesis (Ha): The slope coefficient is not equal to 1 (β1 ≠ 1)

Using the t-test approach, we can calculate the t-statistic for the slope coefficient. The estimated coefficient for the slope is 0.73, and the standard error is 0.10.

t-statistic = (0.73 - 1) / 0.10 ≈ -2.70

Looking up the critical value in the t-table at a 5% level of significance for a two-tailed test, we find that the critical value is approximately 2.000.

Since the calculated t-statistic (-2.70) is greater in magnitude than the critical value (2.000), we reject the null hypothesis. Therefore, there is sufficient evidence to suggest that the slope coefficient is not equal to 1.

(c) Using the p-value approach for part (b)-(i), we compare the p-value associated with the coefficient of intercept to the chosen level of significance (1%). If the p-value is less than 0.01, we reject the null hypothesis.

(d) Using the p-value approach for part (b)-(ii), we compare the p-value associated with the slope coefficient to the chosen level of significance (5%). If the p-value is less than 0.05, we reject the null hypothesis.

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Answer:

Step-by-step explanation:

when we find the volume of a cylinder we must know

the radius

the length of the cylinder-L

L^2=11^2+4^2

L^2= 144+16

L=√160

L=4√10 INCHES

                       = 3.14*16*4√10

                       = 3.14*64*2.23*1.41

                       = 632.192528

                       ≈632 CUBIC INCHES

The equation that represent amount of oil in the tank at x minutes is

6- 0.2t

A mathematical statement that shows that two mathematical expressions are equal.

Given:

rate of filling the tank = 0.2 feet/ minute

After 15 minutes,

height = 6 feet

let the time take be x minutes

So, the equation that represent amount of oil in the tank at x minutes.

=6- 0.2t

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Answer:

10.8 m²

Step-by-step explanation:

To find area, we do 3.14*r^2

since diameter = 2 radius divide each by 2

2 and 0.75

A outer= 3.14*2^2

3.14*4

12.56 m²

A inner = 3.14*0.75^2

≈1.8 m²

to find the shaded area subtract the outer from the inner

12.56-1.8=10.76

which rounds up to

10.8 m²

If we use π then we get

about

12.57

and

1.77

subtract to get

10.8 m²

The defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3​-sigma  The upper control limit (UCL) is approximately 0.0450.

The upper control limit (UCL) for a 3-sigma control chart is given by:

\(\[UCL\) = defect rate + 3 * sqrt((defect rate * (1 - defect rate)) / sample size)

Substituting the values, where the defect rate is 1.50% (0.015) and the sample size is 200, we get:

\(\[UCL = 0.015 + 3 \times \sqrt{\frac{0.015 \times (1 - 0.015)}{200}}\]\)

Calculating this expression, we find:

\(\[UCL \approx 0.0450\]\)

Therefore, the upper control limit (UCL) is approximately 0.0450.

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Answer:

y^2-(28/7)

or, y^2-(4)

The average sample proportion for all possible samples of 161 flips of the coin is 0.45. The standard deviation of the population consisting of these sample proportions is approximately 0.027, and the variance is approximately 0.000729.

To find the mean (μ_p^) of the sample proportions, we use the true probability of getting tails, which is 0.45. Since the sample size is 161, the average sample proportion for all possible samples of 161 flips is also 0.45.

The standard deviation (σ_p^) and variance (σ_p^2) of the population consisting of these sample proportions, we can use the formula for the standard deviation of a sample proportion:

σ_p^ = √[(p_hat * (1 - p_hat)) / n]

where p_hat is the sample proportion and n is the sample size. In this case, p_hat is equal to 0.45 (the true probability of getting tails), and n is 161.

Plugging these values into the formula, we get:

σ_p^ = √[(0.45 * (1 - 0.45)) / 161]

     ≈ 0.027

So, the standard deviation of the population of sample proportions is approximately 0.027.

The variance can be obtained by squaring the standard deviation:

σ_p^2 ≈ (0.027)^2 ≈ 0.000729

Therefore, the variance of the population of sample proportions is approximately 0.000729.

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The equation of the tangent plane to the surface defined by the function z = 2x² + y² at point (1, 2) is 4(x - 1)+4(y - 2)-(z - 9) = 0.

To find the equation of the tangent plane to the surface z = 2x² + y² at point (1, 2), we need to use partial derivatives.

First, we find the partial derivatives of z with respect to x and y,

∂z/∂x = 4x

∂z/∂y = 2y

Then, we evaluate these partial derivatives at the point (1, 2),

∂z/∂x (1, 2) = 4(1) = 4

∂z/∂y (1, 2) = 2(2) = 4

So, the normal vector to the tangent plane at point (1, 2) is:

n = <4, 4, -1>

(Note that the negative sign in the z-component is because the tangent plane is below the surface at this point.) To find the equation of the tangent plane, we use the point-normal form,

n · (r - r0) = 0,  position vector is r, <x, y, z>, r0 is the point of tangency <1, 2, f(1,2)>, and · denotes the dot product.

Substituting in the values we have,

<4, 4, -1> · (<x, y, z> - <1, 2, 9>) = 0

Expanding the dot product and simplifying,

4(x - 1)+4(y - 2)-(z - 9) = 0

This is the equation of the tangent plane to the surface z = 2x² + y² at point (1, 2).

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Answer:

i. Cell phone cases

  Airpods

ii. x + y = 20 .............. 1

10.98x + 27.98y = 355.60 .............. 2

iii. x = 12, and y = 8

Step-by-step explanation:

Amount of sale = $355.60

Cost of Cell phone cases = $10.98

Cost of Airpods = $27.98

Number of phone accessories sold = 20

1. The variables to be considered in the question are:

i. Cell phone cases

ii. Airpods

2. Let the number of cell phone cases bought be represented by x, and that of airpods be represented by y.

Thus,

x + y = 20 .............. 1

10.98x + 27.98y = 355.60 .............. 2

From equation 1,

x = 20 -y

substitute the value of x in equation 2

10.98(20 - y) + 27.98y = 355.60

219.6 -10.98y + 27.98y = 355.60

17y = 136.60

y = \(\frac{136.60}{17}\)

y = 8.0353

So that,

x = 20 -y

  = 20 - 8.0353

x = 11.9647

Thus,

x = 12, and y = 8

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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The relative frequency of A class guests is 30%, the relative frequency of B class guests is 45%, and the relative frequency of C class guests is 25%.

In statistics, the phrase "relative frequency" refers to the proportion or percentage of times an event or category occurs in a sample or population. By dividing the total number of observations or items in the sample or population by the frequency with which the event or category occurs, it is determined. In data analysis and probability, relative frequency is frequently used to evaluate the occurrence of various occurrences or categories and draw conclusions about the underlying distribution or probabilities of the data.

Given, the total number of guest = 200.

The relative frequency for each class is thus,

Relative frequency of A class guests = 60/200 = 0.3 or 30%

Relative frequency of B class guests = 90/200 = 0.45 or 45%

Relative frequency of C class guests = 50/200 = 0.25 or 25%

Hence, the relative frequency of A class guests is 30%, the relative frequency of B class guests is 45%, and the relative frequency of C class guests is 25%.

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The complete question is:

The average time a molecule spends in its reservoir is known as the residence time.

Residence time is an important concept in environmental science, particularly in the study of water quality and pollution. It refers to the average amount of time that a substance, such as a molecule or a pollutant, spends in a particular environment before it is either removed or transformed. For example, in a river, the residence time of a pollutant would be the amount of time it takes for that pollutant to be either broken down by natural processes or transported downstream to another location. By understanding residence time, scientists can better predict how pollutants will move through the environment and where they are likely to accumulate.

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The volume of the solid obtained by rotating the region enclosed by y=x², x=y² about the line x=−7 can be computed using the method of discs or washers via an integral.

The given region enclosed by y=x², x=y² can be represented as:

As we need to rotate the region about the line x = -7, then we need to perform the following transformation:

x = t - 7So, the region enclosed by y=x², x=y² can be represented as:

y = (t - 7)², t = y²

The limits of integration of the variable 't' will be a = 0 and b = 1

As we are using the method of cylindrical shells, then the volume of the solid obtained can be represented as:

V = 2π∫₀¹ (y)(t(y)) dy

where, (y)(t(y)) = (t - 7)²

The integral can be written as:

V = 2π∫₀¹ (t - 7)² dy

By substituting t = √y, we have the following:

dt/dy = 1/2y^(-1/2)

Therefore, the integral becomes:

V = 2π∫₀¹ (t - 7)²

dy= 2π∫₀¹ (√y - 7)²

dy= 2π∫₀¹ y - 14√y + 49

dy= 2π[(1/2)y² - (28/3)y^(3/2) + 49y] from 0 to 1

By substituting the limits of integration a = 0 and b = 1, we have:

V = 2π[(1/2) - (28/3) + 49] = 2π[97/6]

Therefore, the volume of the solid obtained is V = 97π/3 square units.

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The estimated position of the particle at t = 4.2 is 8.6 meters. The maximum possible error in the linearization at t = 4.2 is 0.05 meters.

(a) To estimate the position of the particle at t = 4.2, we can use the linearization of s(t) at t = 4:

s(t) ≈ s(4) + v(4)(t - 4)

Plugging in s(4) = 8 and v(4) = 3, we get:

s(t) ≈ 8 + 3(t - 4)

At t = 4.2, we have:

s(4.2) ≈ 8 + 3(4.2 - 4)

≈ 8.6

Therefore, the estimated position of the particle at t = 4.2 is 8.6 meters.

(b) The error in the linearization is given by:

Error = s(4.2) - L(4.2)

where L(4.2) is the value of the linearization at t = 4.2. Using the linearization formula from part (a), we have:

L(t) = 8 + 3(t - 4)

L(4.2) = 8 + 3(4.2 - 4)

= 8.6

Therefore, the maximum possible error is given by:

\(|Error| ≤ max{|s''(t)|} * |(4.2 - 4)^2/2|\)

where |s''(t)| is the maximum absolute value of the second derivative of s(t) on the interval [4, 4.2]. We know that the acceleration satisfies |a(t)| < 10 m/s^2 for all times, so we have:

\(|s''(t)| = |d^2s/dt^2| ≤ 10\)

Plugging in the values, we get:

\(|Error| ≤ 10 * |0.1^2/2|\)

= 0.05

Therefore, the maximum possible error in the linearization at t = 4.2 is 0.05 meters.

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Answer:

Step-by-step explanation:

13x + 47 = 151

subtract 47 from both sides

13x = 104

divide by 13 on both sides

x = 8

Answer:357.96in

Step-by-step explanation:

1. Surface area of a cylindar is A= 2πr(r+h)

2. A= 2·π·3 (3+16)

Second question

Answer: 296in

We know that:

- She has some of it complete, but the robot still needs 3 arms and 6 wheels.

- Patty has saved up $68, which is enough to buy the parts she needs.

- Arms costs $13 and wheels costs $4

We must find how much money is left after making the purchase.

To find it we must subtract the money spent on the purchase from the money saved.

- money spent:

Is the money spent when she buys the arms and the wheels

So, the money spent is equal to $63

- money saved

Is the money Patty has saved.

Patty has saved up $68.

Finally, subtracting the money spent on the purchase from the money saved

ANSWER:

After Patty buys the parts, $5 is left.

Answer:

63.43

Step-by-step explanation:

For this I'll be using tangent, which is an easier way.

tan x = 22/11

x = \(tan^{-1}\) (22/11)

Plug into calculator, you get 63.43.

Answer: 69.9

Step-by-step explanation:

This is a contradiction, which means that there is no solution for the given equation. Therefore, the correct answer is option C, "No solution".

There is only one solution for the given equation.

5 - 3x = 4 + x + 2 - 4x

Simplifying the equation, we get:

5 - 3x = 6 - 3x

Subtracting 6 from both sides, we get:

-1 - 3x = -3x

Adding 3x to both sides, we get:

-1 = 0

A linear equation is an equation that can be written in the form y = mx + b, where y and x are variables, m is the slope, and b is the y-intercept. It represents a straight line on a graph. Linear equations can be used to model a variety of real-world situations, such as the relationship between temperature and time, or the cost of producing a certain quantity of goods.

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We can see that both sides are equal, which means that the equation has infinitely many solutions.

Therefore, the answer is: D. Infinitely many solutions is correct.

To solve for the number of solutions of 5 - 3x = 4 + x + 2 -4x,

we first simplify the equation by combining like terms:

Combine like terms on both sides of the equation:

5 - 3x = 6 - 3x

Compare the coefficients of the x terms:

-3x = -3x

Since both sides of the equation have the same coefficients for the x terms, there are infinitely many solutions.

Therefore, the answer is: D. Infinitely many solutions is correct.

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